+0  
 
+1
40
1
avatar+574 

Let an integer  be bad if there is no way to insert a colon among the digits of  to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to form a time. For example, 100 is good because we can write 1:00, but 164 is bad. How many bad integers between 100 and 200 are equivalent to 3 mod 4?

supermanaccz  Apr 27, 2018
Sort: 

1+0 Answers

 #1
avatar+633 
+3

Hi supermanaccz!

 

So from 100 to 200, we first need to determine what numbers are bad. 

 

From 100 to 159, they are all good, since we can have 1:00 and 1:59.

 

But from 160 to 199, they are all bad. There is no 1:60, since that will be 2 o'clock. 

 

There is no 1: 99.

 

So we need to calculate how many numbers from 160 - 199 are equal to 3 mod 4.

 

The smallest number that is from 160 - 199 that is equal to 3 mod 4 is 163.

 

3 / 4 = 0 R 3

 

163 / 4 = 40 R 3

 

The largest is 199. 

 

199 / 4 = 49 R 3

 

To calculate how many numbers we want from 163 to 199, we do:

 

\((199-163)/3+1=\boxed{13}\)

 

That will be your final answer .

 

I hope this helped, 

 

gavin.

GYanggg  Apr 27, 2018

21 Online Users

avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy